Golden magic: Difference between revisions

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==Scale==

Golden magic approximates simple intervals in the 2,3,7,11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2,3,7,11 subgroup:

Golden magic approximates simple intervals in the 2.3.7.11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2.3.7.11 subgroup:

{| class="wikitable"

|'''Scale Degree'''

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|w8

|}

The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp, and the lowest error is 0.012 cents, for 11/6. Golden magic tempers out the ~~Saluzo comma, a.k.a.~~ [[Pentacircle comma]], as well as the Saquinzo comma. Furthermore, five generators of golden magic equal the perfect fifth in [[Peppermint-24]], and golden magic can be construed as a close rank 2 approximation of Peppermint, with the quasi-diesis being 57.543 cents.

The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp, and the lowest error is 0.012 cents, for 11/6. Golden magic tempers out the [[Pentacircle comma|Saluzo comma]] as well as the Saquinzo comma. Furthermore, five generators of golden magic equal the perfect fifth in [[Peppermint-24]], and golden magic can be construed as a close rank 2 approximation of Peppermint, with the quasi-diesis being 57.543 cents.

The extension of golden magic to the full 11 limit also tempers out the [[Magic comma|Laquinyo comma]], the [[Septimal kleisma|Ruyoyo comma]], the [[Sensamagic comma|Zozoyo comma]], and the [[875/864|Zotriyo comma]].

Golden magic can be extended to the 13 limit by tempering out the [[364/363|Tholuluzo comma]] and the [[praveensma|Thoquadzo comma]]. The 63 tone golden magic MOS has a copy of the 9 tone [[praveensma|praveensmic]] MOS as well as the 18 tone 3-MOS.

== Golden Kite Guitar ==

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A tuning that consists of alternating downmajor thirds at 380.819c and upmajor thirds at 438.362c is recommended as it makes the stretches needed to play 11 limit chords on a Kite guitar more manageable.

== See also ==

* [[Golden sequences and tuning]]

[[Category:104edo]]

[[Category:167edo]]

[[Category:Magic]]

[[Category:Golden ratio]]

[[Category:41-tone scales]]

@@ Line 3: / Line 3: @@
 ==Scale==
-Golden magic approximates simple intervals in the 2,3,7,11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2,3,7,11 subgroup:
+Golden magic approximates simple intervals in the 2.3.7.11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2.3.7.11 subgroup:
 {| class="wikitable"
 |'''Scale Degree'''
@@ Line 306: / Line 306: @@
 |w8
 |}
-The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp, and the lowest error is 0.012 cents, for 11/6. Golden magic tempers out the Saluzo comma, a.k.a. [[Pentacircle comma]], as well as the Saquinzo comma. Furthermore, five generators of golden magic equal the perfect fifth in [[Peppermint-24]], and golden magic can be construed as a close rank 2 approximation of Peppermint, with the quasi-diesis being 57.543 cents.
+The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp, and the lowest error is 0.012 cents, for 11/6. Golden magic tempers out the [[Pentacircle comma|Saluzo comma]] as well as the Saquinzo comma. Furthermore, five generators of golden magic equal the perfect fifth in [[Peppermint-24]], and golden magic can be construed as a close rank 2 approximation of Peppermint, with the quasi-diesis being 57.543 cents.
+The extension of golden magic to the full 11 limit also tempers out the [[Magic comma|Laquinyo comma]], the [[Septimal kleisma|Ruyoyo comma]], the [[Sensamagic comma|Zozoyo comma]], and the [[875/864|Zotriyo comma]].
+Golden magic can be extended to the 13 limit by tempering out the [[364/363|Tholuluzo comma]] and the [[praveensma|Thoquadzo comma]]. The 63 tone golden magic MOS has a copy of the 9 tone [[praveensma|praveensmic]] MOS as well as the 18 tone 3-MOS.
 == Golden Kite Guitar ==
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 A tuning that consists of alternating downmajor thirds at 380.819c and upmajor thirds at 438.362c is recommended as it makes the stretches needed to play 11 limit chords on a Kite guitar more manageable.
+== See also ==
+* [[Golden sequences and tuning]]
+[[Category:104edo]]
+[[Category:167edo]]
+[[Category:Magic]]
+[[Category:Golden ratio]]
+[[Category:41-tone scales]]